This application claims the priority of Korean Patent Application No. 2003-65540, filed on Sep. 22, 2003, in the Korean Intellectual Property Office, the disclosure of which is incorporated herein in its entirety by reference.
1. Field of the Invention
The present invention relates to data encoding and decoding methods and apparatuses for a recording system, an more particularly, to data encoding and decoding methods and apparatuses that have great performance even at a low signal-to-noise ratio.
2. Description of the Related Art
As the integration density or recording systems increases, the signal-to-noise ratio of signals read from the recording systems decreases. Therefore, data detectors for high-density recording systems are now required to have better detection performance than their conventional counterparts. There are a few reliable conventional data detecting methods, i.e., a partial response maximum likelihood method, a noise-predictive maximum likelihood method, and a low-density parity check (LDPC) method, which has better performance than a turbo code decoding method in terms of approaching the Shannon limit.
An LDPC code is a linear block code that encodes data by using an LDPC matrix most of whose elements are “0”s. The performance of the LDPC code is considerably dependent upon the size of the LDPC matrix and the pattern of distribution of “1”s in the LDPC matrix. The LDPC code is decoded using a probability propagation method, which is also known as a belief propagation algorithm.
In order to decode the LDPC code, a likelihood function should be calculated first. In order to calculate the likelihood function, input data should be a signal whose output levels are detectable. However, it is difficult to detect output levels of a signal output from a partial response (PR) equalizer that compensates for a signal reproduced from a recording system, i.e., an output level of a PR channel.
This problem also applies to a turbo-like system used for improving the performance of a storage system. A conventional turbo-like system adopts different decoding techniques for an outer code and an inner code. For example, the conventional turbo-like system uses an LDPC code decoding method to decode an outer code and uses a partial response maximum likelihood (PRML) or non-parametric maximum likelihood (NPML) method to decode an inner code, and the reason is as follows. An LDPC code decoder should receive a signal with detectable output levels as input data so as to perform an LDPC code decoding process. However, as described above, output levels of a signal output from a PR equalizer, i.e., output levels of a PR channel, are hard to detect, which makes it difficult to form the conventional turbo-like system of LDPC codes only in a PR channel.
More specifically, since the output levels of the PR channel are hard to detect, an LDPC code is only used as an outer code. However, due to the characteristics of the LDPC code, a likelihood function should be calculated as a-priori information before decoding the LDPC code. In order to calculate the likelihood function, extrinsic information should be provided from an outer code to an inner code, and the output levels of the PR channel should also be provided. However, the output levels of the PR channel cannot be easily detected and are not provided to the outer code. Therefore, the outer code has to calculate the likelihood function by only using the extrinsic information. Accordingly, the LDPC code decoder may not be able to precisely calculate the likelihood function, and the extrinsic information provided from the outer code to the inner code may be inaccurate.